SEARCH · Engineering Papers

Results for “persistent current”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 307 records · Page 17

All sources NASA NTRS DOE OSTI

NASA NTRSDate not supplied

The Plant Water Management Experiments: Hydroponics 3 & 4

As humans consider longer-duration missions in space, NASA has identified production of fresh vegetables aboard spacecraft as beneficial for crew nutrition, mental wellbeing, and enabling bioregenerative life support (i.e., air, water, and waste processing). Current low-g plant growth techniques have successfully grown a variety of leafy and flowering plants. However, unique microgravity fluidics challenges to maintain plant moisture levels persist which hamper overall system reliability. The Plant Water Management (PWM) experiments seek to demonstrate low-cost, low-mass, reusable plant growth systems that leverage recent advances in low-g capillary fluidics phenomena to provide routine, largely passive, water delivery to plants. This paper presents findings from a series of PWM-Hydroponics 3 & 4 experiments, which were collected during three ISS flight operations that occurred in March, May, and July of 2021. Open hydroponic capillary channel flows with synthetic evapo-transpiring plant models were used. Tests demonstrated flow stability for single and parallel channel flow configurations across a range of flow rates, plant types, and plant arrangements. Technology demonstrations of both passive aeration and bubble phase separation are reported. We provide details of the data reduction and archive. Insights from the successful flight demonstrations provide a foundation from which follow-on PWM-Hydroponics 5 & 6 experiments on ISS, potentially incorporate living plants, are being considered. Xx Summary of positives and negatives..

Marc B. Wasserman↗

NASA NTRS2022

Noble Gases and Stable Isotopes Track the Origin and Early Evolution of the Venus Atmosphere

The composition the atmosphere of Venus results from the integration of many processes entering into play over the entire geological history of the planet. Determining the elemental abundances and isotopic ratios of noble gases (He, Ne, Ar, Kr, Xe) and stable isotopes (H, C, N, O, S) in the Venus atmosphere is a high priority scientific target since it could open a window on the origin and early evolution of the entire planet. This chapter provides an overview of the existing dataset on noble gases and stable isotopes in the Venus atmosphere. The current state of knowledge on the origin and early and long-term evolution of the Venus atmosphere deduced from this dataset is summarized. A list of persistent and new unsolved scientific questions stemming from recent studies of planetary atmospheres (Venus, Earth and Mars) are described. Important mission requirements pertaining to the measurement of volatile elements in the atmosphere of Venus as well as potential technical difficulties are outlined.

noble gases↗

NASA NTRS2014

Investigation of Unsteady Flow Field in a Low-Speed One and a Half Stage Axial Compressor: Effects of Tip Gap Size On the Tip Clearance Flow Structure at Near Stall Operation - Part 2

The primary focus of this paper is to investigate the effect of rotor tip gap size on how the rotor unsteady tip clearance flow structure changes in a low speed one and half stage axial compressor at near stall operation (for example, where maximum pressure rise is obtained). A Large Eddy Simulation (LES) is applied to calculate the unsteady flow field at this flow condition with both a small and a large tip gaps. The numerically obtained flow fields at the small clearance matches fairly well with the available initial measurements obtained at the Johns Hopkins University with 3-D unsteady PIV in an index-matched test facility which renders the compressor blades and casing optically transparent. With this setup, the unsteady velocity field in the entire flow domain, including the flow inside the tip gap, can be measured. The numerical results are also compared with previously published measurements in a low speed single stage compressor (Maerz et al. [2002]). The current study shows that, with the smaller rotor tip gap, the tip clearance vortex moves to the leading edge plane at near stall operating condition, creating a nearly circumferentially aligned vortex that persists around the entire rotor. On the other hand, with a large tip gap, the clearance vortex stays inside the blade passage at near stall operation. With the large tip gap, flow instability and related large pressure fluctuation at the leading edge are observed in this one and a half stage compressor. Detailed examination of the unsteady flow structure in this compressor stage reveals that the flow instability is due to shed vortices near the leading edge, and not due to a three-dimensional separation vortex originating from the suction side of the blade, which is commonly referred to during a spike-type stall inception. The entire tip clearance flow is highly unsteady. Many vortex structures in the tip clearance flow, including the sheet vortex system near the casing, interact with each other. The core tip clearance vortex, which is formed with the rotor tip gap flows near the leading edge, is also highly unsteady or intermittent due to pressure oscillations near the leading edge and varies from passage to passage. For the current compressor stage, the evidence does not seem to support that a classical vortex breakup occurs in any organized way, even with the large tip gap. Although wakes from the IGV influence the tip clearance flow in the rotor, the major characteristics of rotor tip clearance flows in isolated or single stage rotors are observed in this one and a half stage axial compressor.

Unsteady↗

NASA NTRS2005

Forecasting Lightning at Kennedy Space Center/Cape Canaveral Air Force Station, Florida

The Applied Meteorology Unit (AMU) developed a set of statistical forecast equations that provide a probability of lightning occurrence on Kennedy Space Center (KSC) I Cape Canaveral Air Force Station (CCAFS) for the day during the warm season (May September). The 45th Weather Squadron (45 WS) forecasters at CCAFS in Florida include a probability of lightning occurrence in their daily 24-hour and weekly planning forecasts, which are briefed at 1100 UTC (0700 EDT). This information is used for general scheduling of operations at CCAFS and KSC. Forecasters at the Spaceflight Meteorology Group also make thunderstorm forecasts for the KSC/CCAFS area during Shuttle flight operations. Much of the current lightning probability forecast at both groups is based on a subjective analysis of model and observational data. The objective tool currently available is the Neumann-Pfeffer Thunderstorm Index (NPTI, Neumann 1971), developed specifically for the KSCICCAFS area over 30 years ago. However, recent studies have shown that 1-day persistence provides a better forecast than the NPTI, indicating that the NPTI needed to be upgraded or replaced. Because they require a tool that provides a reliable estimate of the daily thunderstorm probability forecast, the 45 WS forecasters requested that the AMU develop a new lightning probability forecast tool using recent data and more sophisticated techniques now possible through more computing power than that available over 30 years ago. The equation development incorporated results from two research projects that investigated causes of lightning occurrence near KSCICCAFS and over the Florida peninsula. One proved that logistic regression outperformed the linear regression method used in NPTI, even when the same predictors were used. The other study found relationships between large scale flow regimes and spatial lightning distributions over Florida. Lightning, probabilities based on these flow regimes were used as candidate predictors in the equation development. Fifteen years (1 989-2003) of warm season data were used to develop the forecast equations. The data sources included a local network of cloud-to-ground lightning sensors called the Cloud-to-Ground Lightning Surveillance System (CGLSS), 1200 UTC Florida synoptic soundings, and the 1000 UTC CCAFS sounding. Data from CGLSS were used to determine lightning occurrence for each day. The 1200 UTC soundings were used to calculate the synoptic-scale flow regimes and the 1000 UTC soundings were used to calculate local stability parameters, which were used as candidate predictors of lightning occurrence. Five logistic regression forecast equations were created through careful selection and elimination of the candidate predictors. The resulting equations contain five to six predictors each. Results from four performance tests indicated that the equations showed an increase in skill over several standard forecasting methods, good reliability, an ability to distinguish between non-lightning and lightning days, and good accuracy measures and skill scores. Given the overall good performance the 45 WS requested that the equations be transitioned to operations and added to the current set of tools used to determine the daily lightning probability of occurrence.

Lambert, Winfred↗

NASA NTRSDate not supplied

Conditions of the Toll-Like Receptors System of the Human Innate Immunity Cells During the Long-Term Isolation

During long duration missions onboard the International Space Station (ISS), alterations in T cell function and plasma cytokine profiles have been observed. Recent studies involving pattern recognition receptors (PRRs) have established that adaptation of innate immunity to long duration space flight occurs through changes in signal PRRs, Toll-like receptors (TLRs). Despite the fact that fundamental research of PRR molecular biology is far from complete, there are an increasing number of arguments confirming the important role of this system in regulating the initial stages of the adaptive immune response, as well as in the formation of autoimmune and allergic diseases. Long duration isolation is widely used by NASA as an analog for space flight with previous missions including several Antarctic bases, an undersea research station (NEEMO), and other isolation chambers. ‘SIRIUS’ is a multi-compartment pressurized facility at the IMBP in Moscow, Russia, in which subjects will spend 8 months executing tasks similar to those performed by astronauts in space. Prolonged isolation studies like SIRIUS replicate many of the influences expected to occur during long duration spaceflight missions including isolation, stress, confinement, and living in remote conditions. The immune study to be performed on the upcoming SIRIUS mission is being led by Dr. Sergey Ponomarev at the Institute of Biomedical Problems in Moscow, Russia. The NASA JSC Immunology lab will provide analysis of immune cell function, serum cytokines and stress hormones, and salivary cortisol, cytokines, and viruses. This study will be conducted with SIRIUS subjects under the auspices of the parent program. The goal of the study is to evaluate the effect of the 8-month isolation mission on components of human innate immunity at the molecular and cellular level. Successful implementation and completion of this project will provide a unique assortment of new data, significantly expanding the current understanding of the molecular and cellular changes in TLRs during long-term isolation. We hypothesize that mission-like isolation in the Russian NEK facility, consisting of circadian misalignment, isolation, stress, and ‘station lifestyle’, will result in a pattern of immune dysregulation similar to that observed in astronauts onboard ISS. This pattern of alterations can be summarized as phenotypic changes (altered distribution of peripheral cytotoxic, central memory, CD8+ T cell subsets), reductions in T cell function, alterations in plasma cytokine profiles (increased inflammatory and certain chemokines), and reductions in mitogen stimulated cytokine profiles (spans Th1, Th2, Th17). We further hypothesize that these immune changes will correlate with the reactivation of latent herpesviruses (which persists during orbital flight), to be used as measurable adverse clinical manifestation or with other observed symptomology. The SIRIUS-21 mission began in November of 2021 and successfully concluded with the crew emerging in July of 2022. Currently, the logistics of shipping the samples from Russia to the United States is being organized.

Cody L Gutierrez↗

DOE OSTI2023

Climate science to inform adaptation policy: Heat waves over India in the 1.5°C and 2°C warmer worlds

Developing a better scientific understanding of anthropogenic climate change and climate variability, especially the prediction/projection of climate futures with useful temporal and geographical resolution and quantified uncertainties, and using that knowledge to inform adaptation planning and action will become crucially important in the coming years. Generating such policy-relevant knowledge may be particularly important for developing countries such as India. It is with this backdrop that, in this paper, we analyze future heat waves in India by using observations and a large number of model simulations of historical, + 1.5 °C, and + 2.0 °C warmer worlds. In both the future scenarios, there is an increased probability of heat waves during June and July when the Indian monsoon is in full swing and humidity is high, which makes the heat events even more of a health risk. While the highest temperatures in heat waves may not increase much in future climates, the duration and areal extent of the heat waves will most likely increase, leading to the emergence of new heat wave-prone zones in India. The results indicate that the joint frequencies of the longest duration and large area events could be nearly threefold greater in the + 1.5 °C and fivefold greater in the + 2.0 °C future scenarios compared to historical simulations. Thus, overall, the study indicates a substantial increase in the risk of heat events that typically elicit warnings from forecasters. The likely widespread and persistent nature of heat wave events in the future, as revealed by this study, will require planning and adaptation measures beyond the short-term disaster planning frameworks currently in place. Exploring what these measures might look like is beyond the scope of this study, but it underlines the importance of developing climate knowledge with high temporal and geographical resolution capable of informing adaptation policy and planning.

+1.5 °C and +2.0 °C↗

DOE OSTI2024

Ferroelectric Al1 − xBxN–GaN heterostructures

This report demonstrates Al0.93B0.7N thin films grown epitaxially on n-type GaN (0002)/c-plane sapphire substrates by reactive magnetron sputtering at 300 °C. At 200 nm film thickness, the Al0.93B0.07N layers exhibit partially relaxed substrate-induced epitaxial strain, a 0.16° wide (0002) rocking curve, in-plane crystallographic registry, and sub-nanometer surface roughness. Electrically, the stack shows robust hysteresis over three frequency decades, a remanent polarization of ∼125 μC/cm2, a strongly frequency dependent coercive field, highly uniform dc leakage currents, and endurance >106 field cycles. This report validates possibilities for ferroelectric nitride integration into conventional III-nitride heterostructures with high crystalline fidelity, high electrical resistivity, and persistent hysteresis. Such materials are synthesizable at thermal budgets and temperatures compatible with back-end-of-the-line boundary conditions.

Physics↗

NASA NTRS1973

Heat treatment effects in Cu2S-CdS heterojunction photovoltaic cells

The optical and electronic properties of single crystal Cu2S-CdS photovoltaic cells were investigated. In these cells trapped charge near the interface which is manifested by a persistent increase in junction capacitance (the photocapacitance) plays a significant role in determining the carrier transport properties. It was found that the severe degradation in short-circuit current observed in heat-treated cells can be separated into two components: (1) a relatively small thermal component occurring on heat-treatment in the dark, and (2) a much larger degradation caused by exposure to light at room temperature. By a short additional heat-treatment above approximately 100 C the cell can be completely restored to its condition before the optically caused degradation with no effect on the depletion layer width.

Fahrenbruch, A. L.↗

NASA NTRS1985

PN velocity beneath Western New Mexico and Eastern Arizona

The experiment involved observing Pn arrivals on an areal array of 7 seismic stations located in the transition zone and along the Jemez lineament. Explosions in coal and copper mines in New Mexico and Arizona were used as energy sources as well as military detonations at White Sands Missile Range, New Mexico, Yuma, Arizona, and the Nevada Test Site. Very preliminary results suggest a Pn velocity of 7.94 km/s (with a fairly large uncertainty) beneath the study area. The Pn delay times, which can be converted to estimates of crustal thickness given knowledge of the velocity structure of the crust increase both to the north and east of Springerville, Arizona. As a constraint on the velocity of Pn, researchers analyzed the reversed refraction line GNOME-HARDHAT which passes through Springerville oriented NW to SE. This analysis resulted in a Pn velocity of 7.9-8.0 km/s for the transition zone. These preliminary results suggest that a normal Pn velocity might persist even though the crust thins (from north to south) by 15 km along the length of the Arizona-New Mexico border. If the upper mantle is currently hot anywhere in western New Mexico or eastern Arizona then the dimensions of the heat source (or sources) might be small compared to the intra-station distances of the seismic arrays used to estimate the velocity of Pn.

Jaksha, L. H.↗

NASA NTRS1986

Analysis of Jovian decametric data: Study of radio emission mechanisms

Catalogues of approx. 200 decametric arcs and approx. 200 gaps between arcs were studied, in an effort to reconcile the data with predictions for the model wherein reflections of Io-induced currents each emit in a conical pattern and yield a distinct radio arc. The most recent interpretations of this data suggest that these Io-produced Alfven waves persist for at least one or two passages of Io, and that the emission cone half angles are approx. 40 to 90 deg., varying from arc to arc. Below 1.2 MHz it was discovered that Jupiter emits radiation strongly modulated in frequency with periods of approx. 200 kHz; this quasi-sinusoidal emission (MSA) can shift more than 180 deg. in phase over periods of 6 seconds, although these shifts are usually much smaller. MSA is not strongly correlated with the longitudes of Io or Jupiter, and typically occurs in patches covering approx. 500 kHz or more for periods of a few minutes. Furthermore, this modulation sometimes resembles a train of impulses in frequency with exponential decays toward high frequencies. Comparison of these results with the previous studies of V-shaped S-bursts is suggestive of an emission mechanism.

Staelin, D. H.↗

NASA NTRS1993

Modeling non-gravitational forces acting on TOPEX/POSEIDON: The early days

TOPEX/POSEIDON is a satellite mission that will use altimetry to make precise measurements of sea-level. The principal goal is to measure sea-level with unprecedented accuracy such that small-amplitude, basin wide sea-level changes caused by large-scale ocean circulation can be detected. To reach this goal, the sensor system and orbit must measure sea-level with decimeter accuracy. This requires that the radial component of the orbit be known to the decimeter level. Orbital errors are dominated by mismodelled gravitational and non-gravitational forces. This paper presents our analysis of non-gravitational forces acting on the satellite during the early days of the mission. Studies were conducted by comparing direct estimates of these forces with observed perturbations in the mean orbital elements. The results show that the satellite is experiencing an unexpected along-track acceleration. Hypotheses range from out-gassing to thruster leaks and drag forces to radiative force. Currently, these issues have not been resolved; however, the evidence suggests that out-gassing was dominant during the first weeks of the mission and that thermal imbalances persist.

Christensen, E. J.↗

DOE OSTI2020

Transcritical diffuse-interface hydrodynamics of propellants in high-pressure combustors of chemical propulsion systems

Rocket engines and high-power new generations of gas-turbine jet engines and diesel engines oftentimes involve the injection of one or more reactants at subcritical temperatures into combustor environments at high pressures, and more particularly at pressures higher than those corresponding to the critical points of the individual components of the mixture, which typically range from 13 to 50 bars for most propellants. This class of trajectories in the thermodynamic space has been traditionally referred to as transcritical. However, the fundamental understanding of fuel atomization, vaporization, mixing, and combustion processes at such high pressures remains elusive. In particular, whereas fuel sprays are relatively well characterized at normal pressures, analyses of dispersion of fuel in high-pressure combustors are hindered by the limited experimental diagnostics and theoretical formulations available. The description of the thermodynamics of hydrocarbon-fueled mixtures employed in chemical propulsion systems is complex and involves mixing-induced phenomena, including an elevation of the critical point whereby the coexistence region of the mixture extends up to pressures much larger than the critical pressures of the individual components. As a result, interfaces subject to surface-tension forces may persist in multicomponent systems despite the high pressures, and may give rise to unexpected spray-like atomization dynamics that are otherwise absent in monocomponent systems above their critical point. In this article, the current understanding of this phenomenon is reviewed within the context of propulsion systems fueled by heavy hydrocarbons. Emphasis is made on analytical descriptions at mesoscopic scales of interest for computational fluid dynamics. In particular, a set of modifications of the constitutive laws in the Navier–Stokes equations for multicomponent flows, supplemented with a high-pressure equation of state and appropriate redefinitions of the thermodynamic potentials, are introduced in this work based on an extended version of the diffuse-interface theory of van der Waals. The resulting formulation involves revisited forms of the stress tensor and transport fluxes of heat and species, and enables a description of the mesoscopic volumetric effects induced by transcritical interfaces consistently with the thermodynamic phase diagram of the mixture at high pressures. Additionally, applications of the theory are illustrated in canonical problems, including dodecane/nitrogen transcritical interfaces in non-isothermal systems. The results indicate that a transcritical interface is formed between the propellant streams that persists downstream of the injection orifice over distances of the same order as the characteristic thermal-entrance length of the fuel stream. The transcritical interface vanishes at an edge that gives rise to a fully supercritical mixing layer.

02 PETROLEUM↗

DOE OSTI2024

Critical Literature Review of Low Global Warming Potential (GWP) Refrigerants and their Environmental Impact

Refrigeration and air conditioning currently account for ~20% of the total electricity consumption in buildings around the world. Over the next three decades as global temperatures are projected to increase, urbanization and economic growth will lead to an increased demand for refrigeration and cooling. Most commonly used refrigerants belong to the five following classes: (i) chlorofluorocarbons, (ii) hydrochlorofluorocarbons, (iii) hydrofluorocarbons (HFCs), (iv) hydrofluoroolefins (HFOs), and (v) natural refrigerants. Over the past century, there have been shifts in which compounds were used for refrigeration to improve safety and durability, allow for ozone protection, and, most recently, to reduce global warming potential (GWP). Although technological advances have led to increased cooling capacity and safer refrigerants, emissions from refrigeration systems can affect the environment by contributing to greenhouse gas emissions or by depleting the ozone layer, depending on the gas emitted. The focus is increasingly on adopting compounds that are both efficient at cooling and effective for reducing emissions and other adverse environmental impacts. Because of policy and regulatory changes to avert ozone depletion and global climate change, much discussion has centered on the environmental impacts of next-generation refrigerants. Of particular interest are the fluorinated refrigerants, HFCs and HFOs, most of which are defined as per- and polyfluoroalkyl substances (PFAS) and their breakdown products (especially trifluoroacetic acid). The US Environmental Protection Agency in 2021 drafted a Strategic Roadmap for PFAS, which has already resulted in an increase in investment in research on these compounds and has restricted the release of PFAS into the environment through the implementation of monitoring and reporting requirements. A critical evaluation of fluorinated refrigerants and their breakdown products with respect to persistence, biodegradation and toxicity, and global warming potential is needed to guide environmental regulations. This document aims to perform a critical review of the relevant scientific data on the most common refrigerants currently used, their degradation products, and their alternatives. Where available, estimates of precursor production quantities and existing environmental regulatory information are reviewed. Key data of interest for the evaluation include physicochemical properties, environmental fate parameters, ecological or human health toxicity/risk information, and GWP for compounds of interest.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Critical Literature Review of Low Global Warming Potential (GWP) Refrigerants and their Environmental Impact

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Doped Mott insulators in the triangular-lattice Hubbard model

Here we investigate the evolution of the Mott insulators in the triangular lattice Hubbard Model, as a function of hole doping δ in both the strong and intermediate coupling limits. Using the advanced density matrix renormalization group (DMRG) method, at light hole doping δ ≲ 10%, we find a significant difference between strong and intermediate couplings. Notably, at intermediate coupling an unusual metallic state emerges, with short ranged spin correlations but long ranged spin-chirality order. Moreover, no clear Fermi surface or wave vector is observed, this chiral metal also exhibits staggered loop current, which breaks the translational symmetry. These features disappear on increasing interaction strength or on further doping. At strong coupling, the 120 degree magnetic order of the insulating magnet persists for light doping, and produces hole pockets with a well-defined Fermi surface. On further doping, δ ≈ 10%~20% SDW order and coherent hole Fermi pockets are found at both strong and intermediate couplings. At even higher doping δ ≳ 20%, the SDW order is suppressed and the spin-singlet Cooper pair correlations are simultaneously enhanced. We also briefly comment on the strong particle-hole asymmetry of the model.

36 MATERIALS SCIENCE↗

NASA NTRS1977

A numerical investigation of the severe thunderstorm gust front

The structure of the thunderstorm gust front is investigated by a nonhydrostatic, two-dimensional (x,z) numerical model. In the model, which is dry, the production of negatively buoyant air by evaporation is parameterized via an externally imposed, local-cooling function. This parameterization sustains a steady cold downdraft, which drives the surface outflow and associated gust front. It is shown that two dominant factors influencing gust front structure in the vertical plane are the solenoidal field coincident with the front and surface friction, modeled by means of a simple bulk aerodynamic drag formulation. The circulation theorem is invoked to illustrate how solenoidal accelerations oppose the deceleration by surface friction. After the onset of a downdraft in the model, these opposing tendencies soon reach a balance. Thus, following a brief transient stage, the model gust front exhibits a persistent configuration as it propagates rapidly forward. The essential features of this configuration are examined and compared with both tower observations of gust fronts and laboratory models of gravity currents.

Mitchell, K. E.↗

NASA NTRS1976

Jupiter's distant environment

Qualitative features of the distant Jovian magnetosphere which have been noted previously are reviewed. These features include the highly deformable or spongy nature of the outer regions, the temporal variability of the middle magnetosphere, the presence of a near-equatorial ring current sheet from about 30 Jupiter radii to the magnetopause and the regular oscillation of particle and field properties associated with planetary rotation. We next add evidence for the persistent presence of a layer of magnetic turbulence in the portion of the magnetosphere just inside the magnetopause and we examine its properties. The importance of the presence of the turbulent layer to theoretical models of the magnetosphere is stressed.

Kivelson, M. G.↗

NASA NTRS1986

Turbulent magnetic reconnection

The results of two-dimensional spectral-method MHD simulations of the effect of turbulence on magnetic-reconnection processes are presented in extensive graphs and tables and characterized in detail. In a periodic sheet-pinch configuration, early-onset, persistent turbulence is found to occur when a low level of broadband fluctuations is introduced into the initial data. Features observed include small-scale unsteady coherent electric-current and vorticity structures, enhanced viscous and resistive dissipation, unsteady and spatially asymmetric fluid flow, large-scale and small-scale magnetic islands, multiple X points, large-amplitude electric-field fluctuations, and spectral characteristics indicating that the turbulence is broadband in both spatial directions and similar to homogeneous MHD turbulence. The importance of reconnection for studies of solar, magnetospheric, and laboratory plasmas in inhomogeneous magnetic fields is indicated.

Matthaeus, W. H.↗